Question: Simplify the following expression: $t = \dfrac{10r^2 + 30r + 20}{r + 1} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ t =\dfrac{10(r^2 + 3r + 2)}{r + 1} $ Then we factor the remaining polynomial: $r^2 + {3}r + {2} $ ${1} + {2} = {3}$ ${1} \times {2} = {2}$ $ (r + {1}) (r + {2}) $ This gives us a factored expression: $\dfrac{10(r + {1}) (r + {2})}{r + 1}$ We can divide the numerator and denominator by $(r - 1)$ on condition that $r \neq -1$ Therefore $t = 10(r + 2); r \neq -1$